Within 3SLS and Between 3SLS. Verify that 3SLS on (7.21) with (left(I_{M} otimes tilde{X}ight)) as the set

Question:

Within 3SLS and Between 3SLS. Verify that 3SLS on (7.21) with $\left(I_{M} \otimes \tilde{X}ight)$ as the set of instruments yields (7.22). Similarly, verify that 3SLS on (7.23) with $\left(I_{M} \otimes \bar{X}ight)$ as the set of instruments yields (7.24). These are the Within 3SLS and Between 3SLS estimators of $\delta_{1}$, respectively.